If you have already executed this:

with(GroupTheory): with(DocumentTools):
lis := SearchSmallGroups('order' = 10 .. 100, 'soluble'):
S := seq(DrawSubgroupLattice(SmallGroup(g), 'highlight' = CompositionSeries(SmallGroup(g))), g in lis[10 .. 20]):

then you could do something like the following,

Tabulate(Matrix(4, 3, [S])):

You can force the issue here by using the symbolic option of simplify and combine. Or you can use an assumption.

See the Help for some description of that symbolic option, here and here.

Sometimes the solve command will produce a "simplified" form (half your goal here).

There is a large set (nonzero measure in the RxR space of m and c) where the expression sqrt(m*c)/m and sqrt(c/m) are not equal. Hence it would hardly be an improvement if those two commands treated these two forms as equivalent, by default. I'd agree that it would be an improvement if the context-menu (context-panel) offered the choice,
   combine(..., symbolic)

Download symbolic.mw

I'm not sure that I fully understand what you mean by "improve" or "best".

You could use the mathfunc type. You could restrict that to not include the elementary functions.

In such a way you could decide up front what you want to accept as "elementary". And presumably that internal list of special functions is updated if something gets added to Maple's stock.

For example, (and this could be tweaked):

Download specf.mw

Another approach is to store the loop index value k and the value of a in a table, and then turn that into a Matrix as a later step.

That allows you to easily handle the situation where some entries are omitted (because, say, they fail some conditional test). You can still have easy access to the accepted indices and values, and plot just those.

Here's an example. There are other ways to accomplish the same thing, some of which are terser, but I've tried to keep it understandable.

Download table_aug_Matrix.mw

I'm not sure how you're expecting the omega(t) values to be used. But this may be a start, or give you some ideas.

The key part here is that I'm using my earlier idea (see Reply above) of using a custom procedure F which can generate each frame.

Once you have such a procedure it is easier to test. You can call it with different arguments and see how it looks. When satisfied you can easily animate it.

[edit] I have adjusted the shape that I plotted with my method.

Download how_rot_ac.mw

By calling parse you turn the strings back into Maple expressions, so naturally when you print them as normal output then you get the same effect as for the original, ie. sequences are pretty-printed with spaces after the commas, whether they are in a list or just as a sequence.

If you want to line-print strings, without the quotation marks appearing, then you could use printf (on the strings, with %s format) instead of print or lprint. Note that conversion to strings might be unnecessary -- your particular goal is still unclear.

If you want to export the entries to an external file then you could use the ExportMatrix command, eg.,
    ExportMatrix("myfile.csv", Matrix([ans1]));
That produces a file named myfile.csv with three lines, each with the entries separated by commas and without spaces. That command has some additional flexibility along those aspects.

What are you actually trying to accomplish with sequences of numbers displayed without spaces after the commas? Are you trying to export it to an external file, for some other software? Or are you going to copy&paste from what is displayed on your Maple GUI?

It is a very common phenomenon on this forum for people to have some task they want to solve, then ask about only part of their approach to solving it, without describing the actual underlying goal or full process that they want. This usually leads to guesswork and unnecessary and inefficient back-and-forth.

In the Maple programming language (1D plaintext, also known as Maple Notation) the word for infinity is:

   infinity

That entry box in the popup is a Maplets TextField, and it expects plaintext Maple Notation.

This seems to be a consequence of the result from DiagonalMatrix having shape=diagonal and storage=diagonal.

A workaround is to force off the compact shape/storage (see two ways, below).

I will submit a bug report.

Download Starnge_ac.mw

Is you lprint the SearchSet you can see that its float values are not what appears in the 2D Input.

I don't know how you managed to get that effect (cut&paste, something with numeric formatting?).

You could re-enter it manually.

But you may still be faced by discrepencies if you expect floats to be matched in the case that they have differing numbers of trailing zeroes.

It might be better if you described precisely what kind of matching you are after, ie. float comparisons to a fixed precision, etc. It may be that verify it a more suitable tool for the comparison, but that depends on what comparison you are after.

Also, you asked about why some sorting occurs. That's how Maple acts with sets of floats. If you don't want them sorted then you could use lists of Vectors instead.

Download Binary_search_ac.mw

An explicitl description of what you're actually trying to accomplish would be a good start to getting best advice.

It would be more helpful and direct if you were to supply the complete example when first submitting the Question.

Hopefully this uses the dsolve solution to produce your line animation in a satisfactory manner.

Download anim_ac.mw

You have b assigned as a Matrix. That's your basic mistake, since you were only indexing into it as b[i], as if it had just one dimension.

Try making it b as a Vector instead, ie,

   b := Vector(3, [-1, 7, -7]);

Below, I have removed also the loading of the VectorCalculus package since that rebinds the Vector command which is hardly useful here. I changed the call of Norm to be explicitly a call to LinearAlgebra:-Norm.

I suggest that you check that it works as you intended.

Download code_zeineb_ac.mw

It is not necessary to write M:-Pn instead of just Pn (for each n), in the situation you describe.

In my experience is far more common to write the references as just Pn in equivalent situations.

You wrote that using the form M:-Pn somestimes "...saved me a lot of trouble". What trouble was that?

If you store them properly (in a .mla Maple Library Archive file) then you wouldn't need to read any of them in each session you want to access them, and they could all get seen as easily as each other.

To access any of them you'd simply need libname to be augmented with the location of the new personal .mla Library file.

- You could augment libname in a worksheet's Startup code, which would affect just that worksheet.
- Or you could augment libname in a personal initialization file.
- Alternatively you could put the .mla Library file under a new folder with a name like whatever the following returns, and have Maple automatically augment libname upon relaunch:
    cat(kernelopts(':-homedir'),"/maple/toolbox/mypackage/lib")

Personally, I think that reading in the plaintext source files each time you want to run a session or worksheet is an unnecessary, overly complicated burden.

But if for some strange reason I was unable to use an .mla file, then I'd probably just create a single .mpl text file that contained the means to input all the individual procedures. That could contain various (say, five) read calls for each of the individual source files, or it could contain the definition of a package module that accessed the individual sources with, say, the $include directive. In this scenario I could subsequently issue one read call of that master (build) file, and all would be avaliable.

[edit] There is an example of writing a module using the $include directive (and the preprocessor) for its member procedures in Section 11.4 of the Programming Guide.

You may well be satisfied with the right-click context-menu approach.

By the way, there is a Help page for that (it takes a little while to fully load and focus on the approriate section in my webbrowser).

Using the result in the left-hand side of an assignment requires mouse actions to copy&paste, so using the mouse to convert to Atomic Variable may be fine.

If you're interested, your expression can also be converted programmatically:

Download atomicvar_constr.mw

ps. In versions before Maple 2017 an Atomic Variable was called an Atomic Identifier.

Try

   ':-b' = b

using single right-ticks (a.k.a. uneval quotes).

The LHS of that equation is an unevaluated reference to the global name b (and not the procedure test1's parameter by a similar name). The RHS evaluates to the value you want to pass along.

test1:=proc(a::posint, {b::posint:=1})::posint:
	return a + b:
end proc:

test2:=proc(a::posint, {b::posint:=1} )::posint:
	return a*test1(a, ':-b' = b);
end proc:

test2(2, b=3);
             10

[edit] I much prefer this approach over using _options['b'], which Joe has suggested.